Robot and Multibody Dynamics Analysis and Algorithms
Robot and Multibody Dynamics: Analysis and Algorithms provides a comprehensive and detailed exposition of a new mathematical approach, referred to as the Spatial Operator Algebra (SOA), for studying the dynamics of articulated multibody systems. The appro
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Abhinandan Jain
Robot and Multibody Dynamics Analysis and Algorithms
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Abhinandan Jain Ph.D. Jet Propulsion Laboratory 4800 Oak Grove Drive Pasadena, California 91109 USA [email protected]
ISBN 978-1-4419-7266-8 e-ISBN 978-1-4419-7267-5 DOI 10.1007/978-1-4419-7267-5 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2010938443 c Springer Science+Business Media, LLC 2011 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
In memory of Guillermo Rodriguez, an exceptional scholar and a gentleman.
To my parents, and to my wife, Karen.
Preface
“It is a profoundly erroneous truism, repeated by copybooks and by eminent people when they are making speeches, that we should cultivate the habit of thinking of what we are doing. The precise opposite is the case. Civilization advances by extending the number of important operations which we can perform without thinking about them. Operations of thought are like cavalry charges in a battle – they are strictly limited in number, they require fresh horses, and must only be made at decisive moments.” Alfred North Whitehead
Robotics, and its need for real-time control, has expanded research in multibody dynamics beyond modeling and systematic formulations, to computational and control issues. While significant progress has been made in these areas, the mathematical complexity of the system dynamics, and the paucity of analytical concepts and mathematical tools to manage the complexity, present imposing challenges. The body of work known as the spatial operator algebra (SOA) provides such analytical and mathematical techniques that address these challenges. The SOA provides spatial operator mathematical constructs, that concisely describe the system dynamics and enable dynamics analysis in a unified and general setting. That the equations of multibody dynamics can be described by an algebra of spatial operators is certainly of mathematical interest. However, the SOA also provides the means to manipulate at a high level of abstraction the equations describing multibody behavior. The significance of this goes beyond the mathematics and is useful in a practical sense. At any stage of the manipulation of equations, spatially recursive algorithms to implement the operator expr
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